Physical quantities and units by Sukesh Kamath

sukeshkamath — 2016-01-22 04:11:17 UTC

sukeshkamath — 2016-01-22 04:11:28 UTC

QUANTITIES, UNITS AND MEASUREMENT

sukeshkamath — 2016-01-22 04:13:42 UTC

QUANTITY -are measurable e.g. mass length, time temperature , current magnetic field strength, force, volume etc.

EQUATION - relates quantities e.g F = ma shows that force is equal to mass X acceleration.

UNITS - show the size of a quantity compared with a standard measurement of that quantity. e.g one newton is the standard force that causes a mass of one kilogram to accelerate by one meter per second

Physical quantities and base units

sukeshkamath — 2016-01-22 04:23:55 UTC

Quantity	Definition	Formula	BaseUnits	Dimensions
Length or Distance	fundamental	d	m (meter)	L (Length)
Time	fundamental	t	s (second)	T (Time)
Mass	fundamental	m	kg (kilogram)	M (Mass)
Area	distance²	A = d²	m²	L²
Volume	distance³	V = d³	m³	L³
Density	mass / volume	d = m/V	kg/m³	M/L³
Velocity	distance / time	v = d/t	m/s c (speed of light)	L/T
Acceleration	velocity / time	a = v/t	m/s²	L/T²
Momentum	mass × velocity	p = m·v	kg·m/s	ML/T
Force Weight	mass × acceleration mass × acceleration of gravity	F = m·a W = m·g	N (newton) = kg·m/s²	ML/T²
Pressure or Stress	force / area	p = F/A	Pa (pascal) = N/m² = kg/(m·s²)	M/LT²
Energy or Work Kinetic Energy Potential Energy	force × distance mass × velocity² / 2 mass × acceleration of gravity × height	E = F·d KE = m·v²/2 PE = m·g·h	J (joule) = N·m = kg·m²/s²	ML²/T²
Power	energy / time	P = E/t	W (watt) = J/s = kg·m²/s³	ML²/T³
Impulse	force × time	I = F·t	N·s = kg·m/s	ML/T
Action	energy × time momentum × distance	S = E·t S = p·d	J·s = kg·m²/s h (quantum of action)	ML²/T
Angle	fundamental	θ	° (degree), rad (radian), rev 360° = 2π rad = 1 rev	dimensionless
Cycles	fundamental	n	cyc (cycles)	dimensionless
Frequency	cycles / time	f = n/t	Hz (hertz) = cyc/s = 1/s	1/T
Angular Velocity	angle / time	ω = θ/t	rad/s = 1/s	1/T
Angular Acceleration	angular velocity / time	α = ω/t	rad/s² = 1/s²	1/T²
Moment of Inertia	mass × radius²	I = m·r²	kg·m²	ML²
Angular Momentum	radius × momentum moment of inertia × angular velocity	L = r·p L = I·ω	J·s = kg·m²/s ћ (quantum of angular momentum)	ML²/T
Torque or Moment	radius × force moment of inertia × angular acceleration	τ = r·F τ = I·α	N·m = kg·m²/s²	ML²/T²
Temperature	fundamental	T	°C (celsius), K (kelvin)	K (Temp.)
Heat	heat energy	Q	J (joule) = kg·m²/s²	ML²/T²
Entropy	heat / temperature	S = Q/T	J/K	ML²/T²K
Electric Charge +/-	fundamental	q	C (coulomb) e (elementary charge)	Q (Charge)
Current	charge / time	i = q/t	A (amp) = C/s	Q/T
Voltage or Potential	energy / charge	V = E/q	V (volt) = J/C	ML²/QT²
Resistance	voltage / current	R = V/i	Ω (ohm) = V/A	ML²/Q²T
Capacitance	charge / voltage	C = q/V	F (farad) = C/V	Q²T²/ML²
Inductance	voltage / (current / time)	L = V/(i/t)	H (henry) = V·s/A	ML²/Q²
Electric Field	voltage / distance force / charge	E = V/d E = F/q	V/m = N/C	ML/QT²
Electric Flux	electric field × area	Φ_E = E·A	V·m = N·m²/C	ML³/QT²
Magnetic Field	force / (charge × velocity)	B = F/(q·v)	T (tesla) = Wb/m² = N·s/(C·m)	M/QT
Magnetic Flux	magnetic field × area	Φ_M = B·A	Wb (weber) = V·s = J·s/C	ML²/QT

Prefiex

sukeshkamath — 2016-01-22 04:35:23 UTC

SI base units to check the homogeneity of physical equations

sukeshkamath — 2016-01-22 04:47:58 UTC

Each side of an equation must have the same base units

F = m x a

[N] = [kg] [ms^-2]

[mkgs^-2] = [kg] [ms^-2]

Make reasonable estimates of physical quantities included within the syllabus

sukeshkamath — 2016-01-22 04:50:02 UTC

an estimate does not have to be exactly correct and often just expresses an order of magnitude.

e.g. The mass of universe is ~10⁵⁰ kilograms

Distinguish between scalar and vector quantities andgive examples of each

sukeshkamath — 2016-01-22 04:52:48 UTC

Vector: Quantity with both magnitude and direction

Scalar: Quantity with only magnitude

Add and subtract coplanar vectors

sukeshkamath — 2016-01-22 05:13:10 UTC

Represent a vector as two perpendicular components

sukeshkamath — 2016-01-22 05:15:48 UTC